\batchmode
\documentclass[12pt,a4paper]{report}
\RequirePackage{ifthen}


\usepackage[utf8x]{inputenc}
\pagestyle{headings}
\usepackage[top=25mm,bottom=25mm,left=40mm,right=25mm]{geometry}
\usepackage{ucs}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{fancybox}
\title{C++ library for symbolic manipulation} 
\author{J\'an Majdan}


\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[latin1]{inputenc}



\makeatletter

\makeatletter
\count@=\the\catcode`\_ \catcode`\_=8 
\newenvironment{tex2html_wrap}{}{}%
\catcode`\<=12\catcode`\_=\count@
\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname #1\endcsname}%
\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname #1\endcsname{}%
  \expandafter\renewcommand\csname #1\endcsname}%
\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
\let\newedcommand\renewedcommand
\let\renewedenvironment\newedenvironment
\makeatother
\let\mathon=$
\let\mathoff=$
\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
\newbox\sizebox
\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
\setlength{\textwidth}{349pt}
\newwrite\lthtmlwrite
\makeatletter
\let\realnormalsize=\normalsize
\global\topskip=2sp
\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
\def\@float{\let\@savefreelist\@freelist\real@float}
\def\liih@math{\ifmmode$\else\bad@math\fi}
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
\let\@largefloatcheck=\relax
\let\if@boxedmulticols=\iftrue
\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
 \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
 \def\phantompar{\csname par\endcsname}\normalsize}%
\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }%
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
 \let\ifinner=\iffalse \let\)\liih@math }%
\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
 \expandafter\box\next\egroup}%
\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
\newcommand\lthtmllogmath{\dimen0\ht\sizebox \advance\dimen0\dp\sizebox
  \ifdim\dimen0>.95\vsize
   \lthtmltypeout{%
*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95 vsize ***}%
   \ht\sizebox.95\vsize \dp\sizebox\z@ \fi
  \lthtmltypeout{l2hSize %
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
       \lthtmlmathtype{#1}\lthtmlvboxmathA}%
\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
       \let\@savefreelist\@freelist \lthtmlhboxmathB}%
\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
       \global\let\@freelist\@savefreelist}%
\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
  \lthtmldisplayA{#1}\let\@eqnnum\relax}%
\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
  \vrule height1.5ex width0pt }%
\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
\newcommand\lthtmlindisplaymathZ{\egroup %
  \centerinlinemath\lthtmllogmath\lthtmlsetmath}
\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
  \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
  \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
  \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\centerinlinemath{%
  \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
  \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 
 \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}

\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize 
  \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
  \else\expandafter\vss\fi}%
\providecommand{\selectlanguage}[1]{}%
\makeatletter \tracingstats = 1 
\providecommand{\Beta}{\textrm{B}}
\providecommand{\Mu}{\textrm{M}}
\providecommand{\Kappa}{\textrm{K}}
\providecommand{\Rho}{\textrm{R}}
\providecommand{\Epsilon}{\textrm{E}}
\providecommand{\Chi}{\textrm{X}}
\providecommand{\Iota}{\textrm{J}}
\providecommand{\omicron}{\textrm{o}}
\providecommand{\Zeta}{\textrm{Z}}
\providecommand{\Eta}{\textrm{H}}
\providecommand{\Nu}{\textrm{N}}
\providecommand{\Omicron}{\textrm{O}}
\providecommand{\Tau}{\textrm{T}}
\providecommand{\Alpha}{\textrm{A}}


\begin{document}
\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
\makeatletter
\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
\lthtmltypeout{}%
\makeatother
\setcounter{page}{1}
\onecolumn

% !!! IMAGES START HERE !!!

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3739}%
$ a(2+a)^{3b}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3745}%
$ A \DOTSB \relbar \joinrel \rightarrow B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3747}%
$ X \mathrel {\dabar@ \dabar@ \mathchar "044B}Y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3755}%
$ \frac  {(x-1)(x^2-3x+2)}{x-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3757}%
$ x=2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3759}%
$ x=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3763}%
$ \infty $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap3768}%
\includegraphics[scale=0.6]{logo.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}



\setbox%



\setbox%



\setbox%

\stepcounter{chapter}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3782}%
$ 2+x+Sin(x)+Sin(x)-3-5x \  \approx \  -1-4x+2Sin(x)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3784}%
$ 2x3(-x)+\frac{(y+3)z(3+y)^w}{z^3} \  \approx \  -6x^2+\frac{(3+y)^{1+w}}{z^2} $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3786}%
$ 2+Cos(Sin(0)) \  \approx \  3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3788}%
$ 3-x-3+(x+z)(23+y)Sin(0) \  \approx \  -x $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3790}%
$ x^{5-x-3+x}+(x^2+2)^{x/x}+2+(3x)^0 \  \approx \  5+2x^2 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3792}%
$ x^{4+a}(-y^3)x^by^{-2} \  \approx \  x^{4+a+b}(-y)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3794}%
$ ({x^3})^c+{\left((y+2)^2\right)}^{b+1} \  \approx \  x^{3c}+(2+y)^{2(1+b)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3799}%
$ x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3801}%
$ -x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3803}%
$ 1+x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3805}%
$ 1-x,1+x,1-x,\ldots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3808}%
$ (x(y-\frac{1}{x})+y-y(x-\frac{1}{y})-x)(-x-y)(-1) \  \approx \  y^2-x^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3810}%
$ (x+y)^2(3+x^5)(y^x+x^y) \  \approx \  3x^{2+y}+x^{7+y}+3y^{2+x}+6xy^{1+x}+3x^2y^x+x^7y^x+3x^yy^2+6x^{1+y}y+2x^{6+y}y+x^5y^{2+x}+2x^6y^{1+x}+x^{5+y}y^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3812}%
$ (3+a+b)^{100}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3815}%
$ (f+g)' = f'+ g'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3817}%
$ (fg)' = f'g+ fg'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3819}%
$ (\frac{1}{f})' = \frac{-f'}{f^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3821}%
$ (f\circ g)' = (f'\circ g)g'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3824}%
$ f(x)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3826}%
$\displaystyle \sum_{k=0}^\infty\frac{f^{(k)}(a)}{k!}(x-a)^k.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3830}%
$ 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure368}%
\begin{figure}\centering
\begin{verbatim}

Expr a("a");
Expr b("b");
Expr c(31);
Expr d(2.756);
Expr e(1,"2345843908598538589589684096/23568348753753495839");
Expr f(2*a-b+Sin(a));\end{verbatim}

	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3848}%
$ (+,-)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3850}%
$ (+,-,*,/,\hat{~})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3852}%
$ \hat{~}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure386}%
\begin{figure}\centering
\begin{verbatim}

Expr g(a*((2+a)^(3*b)));
Expr h(a*Power(2+a,3*b));\end{verbatim}

	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure398}%
\begin{figure}\centering
\begin{verbatim}

Expr a("a"), b("b"), c("c"), g("g");
g = 2*a + c*Sin(pi/2) - a*b*(c-1);
std::cout << g.str() << std::endl;
g = 3*a/2 - Power(Ln(a), 2);
std::cout << g.str() << std::endl;\end{verbatim}

	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure408}%
\begin{figure}\texttt{Expr x("x"), y("y"), z("z");\\}
\texttt{Expr a(x+y+z);\\a.sub(x, y);} \\
\textit{// $x+y+z \longrightarrow 2y+z$}\\
\texttt{Expr a(3*x+2*z-z*x+y/(y\^{}x));\\a.sub(x, 1);} \\
\textit{// $3x+2z-zx+y/y^x \longrightarrow 4+z$}\\
\texttt{Expr a(4*x*(x+y)*z);\\a.sub(-2*x, y);} \\
\textit{// $4xz(x+y) \longrightarrow -y^2z $}\\
\texttt{Expr a(4*(Cos(x-y)+(Sin(y-x)*(x-y)+z)*(y-x+z));\\a.sub(x-y, pi/2);}\\
 \textit{// $4(cos(x-y)+((sin(y-x)(x-y)+z)(y-x+z))) \longrightarrow 4(z-\pi/2)^2$}\\
\texttt{Expr a(sin(1-(Power(x,-y)*((x+y)/z));\\a.sub((x+y)/z, x\^{}y);} \\
\textit{// $sin(1-x^{-y}*(\frac{x+y}{z})) \longrightarrow 0$}\\
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure430}%
\begin{figure}\texttt{Expr x("x"), e(2+x);\\e.sub(3+x, x);}
\textit{// $2+x \longrightarrow -1+x \longrightarrow -4+x \longrightarrow$\  \ldots }\\
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure442}%
\begin{figure}\begin{displaymath} \underbrace{x(2+\overbrace{y(a+\underbrace{b(2+x)}_\text{third level})(a-b)}^\text{second level})}_\text{first level}+
\underbrace{(x+sin(cos(x^{\overbrace{2(a-x)}^\text{second level}})))^2(\overbrace{2(\underbrace{a(b+c)}_\text{third level}+x)}^\text{second level})}_\text{first level}\end{displaymath}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure456}%
\begin{figure}\texttt{Expr a("a"), b("b"), c("c"), d("d");\\
		Expr e(a*(1-Power(b-c, 3*(a-d))+d*(2+a+3*(b-c))));}\\\textit{$ // \longrightarrow a(1-(b-c)^{3(a-d)}+d(2+a+3(b-c)))$}\\
		\texttt{Expr e1(e), e2(e), e3(e);}\\
		\texttt{e1.expansion(1);}\textit{$// \longrightarrow a-a(b-c)^{3(a-d)}+ad(2+a+3(b-c))$}\\
		\texttt{e2.expansion(2);}\textit{$// \longrightarrow a+2ad+a^2d+3ad(b-c)-a(b-c)^{3a-3d}$}\\
		\texttt{e3.expansion(3);}\textit{$// \longrightarrow a+2ad+3abd-3acd+a^2d-a(b-c)^{3a-3d}$}\\
		\texttt{e.expansion();}\textit{$ // \longrightarrow a+2ad+3abd-3acd+a^2d-a(b-c)^{3a-3d}$}\\
		\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure476}%
\begin{figure}		\texttt{Expr a("a"), b("b"), c("c"), x("x");}\\
		\texttt{Expr e(a*Sin(x/2)/x-(x\^{}3)*(x-10)); \\e.diff(x);}\\
		\textit{$ // (\frac{a}{x}sin(\frac{x}{2})-x^3(x-10))' ==  -x^3+3x^2(10-x)+\frac{a}{2x}cos(\frac{x}{2})-\frac{a}{x^2}sin(\frac{x}{2})$}\\
		\texttt{e = Power((x+y),(2*x+3))*2*x; \\e.diff(x);}\\
		\textit{$// (2x(x+y)^{3+2x})' == 2((x+y)^{3+2x}+x(x+y)^{3+2x}(2ln(x+y)+\frac{(3+2x)}{x+y})) $}\\
		\texttt{e = 2*x*x*y*Ln(x)+(a\^{}x); \\e.diff(x);}\\
		\textit{$// (a^x+2x^2yln(x))' ==  a^xln(a)+2(xy+2xyln(x))$}\\
		\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure504}%
\begin{figure}		\texttt{Expr x("x");}\\
		\texttt{e1 = Sin(x).taylorSeries(x, 0, 10));}\\
		\textit{$ // x-\frac{x^3}{6}+\frac{x^5}{120}-\frac{x^7}{5040}+\frac{x^9}{362880}$}\\
		\texttt{e2 = Ln(1-x).taylorSeries(x, 0, 5));}\\
		\textit{$//  -x-\frac{x^2}{2}-\frac{x^3}{3}-\frac{x^4}{4}-\frac{x^5}{5}$}\\
		\texttt{e3 = (Power(x, 3)*Cos(x)/(1-x)).taylorSeries(x, 0, 8));}\\
		\textit{$// x^3+x^4+\frac{x^5}{2}+\frac{x^6}{2}+\frac{13x^7}{24}+\frac{13x^8}{24}$}\\
		\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3888}%
$ sinus$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3890}%
$ cosinus$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3892}%
$ tangent$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3894}%
$ cotangent$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3896}%
$ natural$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3898}%
$ logarithm$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure540}%
\begin{figure}\begin{verbatim}

Expr x("x"), y("y");
Expr e(Sin(x)+Cos(x));
e.diff(x);    
Expr f(Ln(Cotg(x*y)-Tg(x));
f.sub(2+y, x);\end{verbatim}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure549}%
\begin{figure}\begin{verbatim}

#include "sympy-cpp.h"
using namespace sympycpp;
Expr mySinus(const Expr & argument) {
    Fx function(argument, "Sinus");
    Expr expression(&function);
    return expression;
}
int main() {
    Expr x("x"), y("y");
    Expr e(2 + 4*x*mySinus(x+y) - x*mySinus((x+2*y-y)));
    e.diff(x);    
    e.sub(y, x);
}\end{verbatim}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3906}%
$\displaystyle 2+3xSinus(x+y)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3908}%
$\displaystyle 3(Sinus(x+y)+xSinus'(x+y)).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure563}%
\begin{figure}\begin{verbatim}

Expr Sinus(const Expr &);
class MySinus: public Fx {
public:
    MySinus(const Expr & e) : Fx(e, "Sinus") {} 	
    virtual Ex * diff(const Sym & x) const {
        Expr e1(Cos(x));
        Expr e2(e_->diff(x), STEALING);
        Expr e3(e1*e2);       
        return e3.innerCopy();
    }
    virtual Ex * copy() const {
        return new MySinus(e_);
    }
    virtual Ex * create(Ex * arg, const allocationPolicy X) const {
        Ex * f = Sinus(arg).innerCopy();
        delete arg;
        arg = 0;
        return f;
    }
};
Expr Sinus(const Expr & e) {
    if (e.str() == "0") {
        return Expr(int(0));
    }
    Ex * args = new MySinus(e);
    return Expr(args, 1);
}\end{verbatim}

\vspace{-5mm}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3919}%
$ x-y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3921}%
$ x+(-y)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3923}%
$ x/y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3925}%
$ x*y^{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3950}%
$ A \longrightarrow B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3952}%
$ X \dashrightarrow Y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap3958}%
\includegraphics[scale=0.3]{strom_ded.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure813}%
\begin{figure}\centering
\begin{description}  		
  \item[Constructor] \hfill \\
  		\texttt{Ex(const type\_info)\\
		 }
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure821}%
\begin{figure}\centering
\begin{description}
  \item[Management of signs] \hfill \\
  	\texttt{Sign sign() const \\
  		void sign(const Sign)\\
  		}
  \item[Identification of types] \hfill \\
  	\texttt{type\_info type() const\\
  		bool isNum() const\\
  		bool isMul() const\\
	  	bool isAdd() const\\
 	 	bool isSym() const\\
  		bool isPow() const\\
  		bool isFx() const\\
  		}
  		\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure830}%
\begin{figure}\centering
\begin{description} 
  \item[Interfaces] \hfill \\
  	\texttt{virtual void treeView(const int i) const}\\
  		\hspace{1cm}\textit{Transformation of expressions into suitable infix trees.}\\
	\texttt{virtual size\_t rsize(const bool all = true) const}\\
  		\hspace{1cm}\textit{Real size (rsize) is a number of elementary subexpressions.}\\
	\texttt{virtual size\_t asize() const}\\
  		\hspace{1cm}\textit{Actual size (asize) is a count of all immediate subexpressions.}\\
	\texttt{virtual size\_t size() const}\\
  		\hspace{1cm}\textit{Count of subexpressions.}\\
	\texttt{virtual std::string str() const}\\
  		\hspace{1cm}\textit{Transformation of an expression into the std::string.}\\
	\texttt{virtual std::string unsigned\_str() const}\\
  		\hspace{1cm}\textit{Transformation of an expression absolute value into the std::string.}\\
	\texttt{virtual Ex * diff(const Sym \&t) const}\\
  		\hspace{1cm}\textit{Differentiation.}\\
	\texttt{virtual Ex * copy ()const}\\
  		\hspace{1cm}\textit{Creation of a new identical expression (a clone).}\\
  		\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure861}%
\begin{figure}
% latex2html id marker 861
\centering
\begin{description}  		
  \item[Special identification of subtypes] \hfill \\
  	\begin{enumerate}
  	\renewedcommand{labelenumi}{(\alph{enumi})}
  		\item
  		\texttt{virtual bool isMultiple() const\\
  				virtual Number Multiplicity () const\\
  		} 
  		\item 
  		\texttt{virtual bool isInteger() const\\
		 	virtual bool isRational() const\\
		 	virtual bool isReal() const\\
		 	}
	\end{enumerate}	 	
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure886}%
\begin{figure}\centering
\begin{description} 
  \item[Constructors] \hfill \\
  	\texttt{Number(const N\_Real \&)\\
		 	Number(const N\_Rational \&)\\
		 	Number(const N\_Real\_init)\\
		 	Number(const N\_Rational\_init)\\
	}
  		\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure896}%
\begin{figure}
% latex2html id marker 896
\centering
\begin{description}  		
  \item[Setting-up of a new value] \hfill \\
  	\begin{enumerate}
  	\renewedcommand{labelenumi}{(\alph{enumi})}
  		\item
  		\texttt{void setToAddition(const Number \&, const Number \&)\\
				void setToSubtraction(const Number \&, const Number \&)\\
				void setToMultiplication(const Number \&, const Number \&)\\
				void setToDivision(const Number \&, const Number \&)\\
  		} 
  			\hspace{1cm}\textit{New stored value is the result of arithmetic operation.}\\
  		\item
  		\texttt{void setValue(const Number \&)\\
				void setValue(const N\_Rational\_init)\\
				void setValue(const N\_Real\_init)\\
				void setValue(const N\_Rational \&)\\
				void setValue(const N\_Real \&)\\
  		}
	  		\hspace{1cm}\textit{Simple setting up.}\\
	  	\item
  		\texttt{void setTFactorial(const int x)\\}
  			\hspace{1cm}\textit{New stored value is factorial of an ingoing parameter.}\\
  	\end{enumerate}	 	
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3990}%
$ <$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3992}%
$ ==$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure918}%
\begin{figure}
% latex2html id marker 918
\centering
\begin{description}  		
  \item[Comparing] \hfill \\
  	\begin{enumerate}
  	\renewedcommand{labelenumi}{(\alph{enumi})}
  		\item 
  		\texttt{bool eq(const N\_Real \&) const\\
				bool eq(const N\_Rational \&) const\\
				bool eq(const N\_Real\_init) const\\
				bool eq(const N\_Rational\_init) const\\
				bool eq(const Number \&) const\\
		}		
		\item		
		\texttt{bool lt(const Number \&) const\\
				bool lt(const N\_Real \&) const\\
				bool lt(const N\_Rational \&) const\\
				bool lt(const N\_Real\_init) const\\
				bool lt(const N\_Rational\_init) const\\
		 }
	\end{enumerate}	 	
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure933}%
\begin{figure}\centering
\begin{description}  		
  \item[Auxiliary functions] \hfill \\
  		\texttt{Number abs() const\\} 
	  		\hspace{1cm}\textit{Absolute value.}\\
  		\texttt{std::string str2() const\\}
	  		\hspace{1cm}\textit{Alternative transformation to std::string, that does not use parentheses.}\\
		\texttt{bool isInt() const\\}
	  		\hspace{1cm}\textit{Is it possible convert Number into int?.}\\
		\texttt{int	getInt() const\\}
	  		\hspace{1cm}\textit{Transformation to int.}\\
		\texttt{void checkVal()\\}
	  		\hspace{1cm}\textit{Verification of a Number value and a relevant mode.}\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure959}%
\begin{figure}\centering
\begin{description}  		
  \item[Constructor] \hfill \\
  		\texttt{Sym(const std::string \&)\\
		 }
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure971}%
\begin{figure}\centering
\begin{description}  		
  \item[Identifier functions] \hfill \\
  		\texttt{std::string title() const\\} 
	  		\hspace{1cm}\textit{Return name/title/identifier of Sym/variable.}\\
  		\texttt{boolean operator==(cons Sym \&) const\\}
		\texttt{boolean operator!=(cons Sym \&) const\\}
	  		\hspace{1cm}\textit{Comparison of Sym by} \texttt{title\_}\textit{ (signs are ignored). }\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4008}%
$ n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4010}%
$ n~\geq~2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap4014}%
\includegraphics[scale=0.3]{addTree2.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1006}%
\begin{figure}\centering
\begin{description}  		
  \item[Construction of addition] \hfill \\
  		\texttt{Add(basic\_container \&v, const allocationPolicy}\texttt{ flag)\\} 
	  		\hspace{1cm}\textit{Special private constructor.}\\
  		\texttt{Add(const Add \&)\\}
		\texttt{virtual Ex * copy() const\\}
	  		\hspace{1cm}\textit{Copying.}\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1023}%
\begin{figure}\centering
\begin{description}  		
  \item[Added functionality] \hfill \\
  		\texttt{bool omit(iterator \& index)\\}
  	  		\hspace{1cm}\textit{Omits one element from addition if possible (more than 2 addends).}\\
		\texttt{bool moreThan1Multiple() const\\}
	  		\hspace{1cm}\textit{Is there more than one multiple addends?}\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4033}%
$ -xy^2(-z)u(-w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4035}%
$ -xy^2zuw$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1041}%
\begin{figure}\centering
\begin{description}  		
  \item[Added functionality] \hfill \\
  		\texttt{virtual Number Multiplicity() const\\}
  	  		\hspace{1cm}\textit{Multiplicity of expressions.}\\
		\texttt{virtual bool isMultiple() const\\}
 			\hspace{1cm}\textit{Is an expression multiple?\\}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap4042}%
\includegraphics[scale=0.3]{mulTree.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1062}%
\begin{figure}\centering
\begin{description}  		
  \item[Construction of Mul] \hfill \\
		\texttt{Mul(const Mul \&, const\_iterator)}\\
		 	\hspace{1cm}\textit{Special constructor that omits one multiplicand.}\\
 		\texttt{Mul(Ex *\& v, Ex *\& x, const allocationPolicy flag)}\\
			\hspace{1cm}\textit{Exploiting constructor.}\\
 		\texttt{Mul(basic\_container \& v, const allocationPolicy flag)}\\
			\hspace{1cm}\textit{Exploiting constructor, which makes multiplication from elements of v.}\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4050}%
$\displaystyle x^{{a_1}^{{a_2}^{\cdot^{\cdot^{\cdot^{a_n}}}}}} = x^{{a_1}{a_2}\ldots{a_n}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1100}%
\begin{figure}\centering
\begin{description}  		
  \item[Construction of powers] \hfill \\
  		\texttt{Pow(const Ex * b, const Ex * e, const allocationPolicy)\\
			 	Pow(Ex * \&, Ex * \&)\\} 
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1113}%
\begin{figure}
% latex2html id marker 1113
\centering
\begin{description}  		
  \item[Auxiliary member functions] \hfill \\
  	\begin{enumerate}
  	\renewedcommand{labelenumi}{(\alph{enumi})}
  		\item
  		\texttt{Ex * copyInverted() const \\} 
  			\hspace{1cm}\textit{Construction of copies that have changed the~sign of the~exponents.}\\
  		\item
  		\texttt{bool isExponentInteger() const\\
				bool isExponentPositive() const\\
				std::string	abs\_Exp\_str() const\\}
	  		\hspace{1cm}\textit{Functions of the exponent.}\\
	  	\item
  		\texttt{void ganef(Ex * \&, Ex * \&, const allocationPolicy)\\}
  			\hspace{1cm}\textit{Exploiting of base and exponent.}\\
  	\end{enumerate}	 	
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1142}%
\begin{figure}\centering
\begin{description}  		
  \item[Construction of Fx] \hfill \\
		\texttt{Fx(const Fx \&)}\\
		 	\hspace{1cm}\textit{Standard copy constructor.}\\
 		\texttt{Fx(const Ex *, const std::string \&)\\
 			Fx(const Expr \&, const std::string \&)}\\
			\hspace{1cm}\textit{Construction of functions by arguments and names.}\\
 		\texttt{Fx(Ex * \&, const std::string \&, const allocationPolicy)}\\
			\hspace{1cm}\textit{Constructor by argument and name, 
			but memory from input expression is exploited for the argument. }\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1158}%
\begin{figure}\centering
\begin{description}  		
  \item[Member functions of Fx] \hfill \\
		\texttt{virtual Ex * copy() const}\\
		 	\hspace{1cm}\textit{Construction of new identical objects in separate memory.}\\
 		\texttt{virtual Ex* create(Ex * \& e, const allocationPolicy) const}\\
			\hspace{1cm}\textit{Construction of new functions.}\\
 		\texttt{std::string name() const }\\
			\hspace{1cm}\textit{Name of the represented function. }\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1178}%
\begin{figure}\centering
\begin{description}  		
  \item[Constructors of Expr] \hfill \\
		\texttt{Expr(const Expr \&)}\\
		 	\hspace{1cm}\textit{Standard copy constructor.}\\
 		\texttt{Expr(const Ex *)\\
 				Expr(Ex * \&, const allocationPolicy)}\\
			\hspace{1cm}\textit{Wrapping of pointers. 
			(the first one makes a copy, the second constructor exploits ingoing memory)}\\
 		\texttt{Expr(const std::string \&)\\
				Expr(const char *)}\\
			\hspace{1cm}\textit{Construction of elementary expressions (variables)}\\
		\texttt{Expr(const int)\\
				Expr(const double)\\
				Expr(const int, const char *)}\\
			\hspace{1cm}\textit{Construction of elementary expressions (numbers).
								The last constructor creates rational numbers from text strings 
								(the first parameter is only a mark that makes this constructor 
								distinguishable from the constructors of variables).}\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1198}%
\begin{figure}\centering
\begin{description}  		
  \item[Functionality of sympy--cpp] \hfill \\
		\texttt{bool expansion(const int level=-1)}\\
		 	\hspace{1cm}\textit{Transformation of multiplication of sums to summation of multiplication.}\\
 		\texttt{void sub(const Expr \& x, const Expr \& y)}\\
			\hspace{1cm}\textit{Substitution of the first parameter }\texttt{x}\textit{ by the second parameter }\texttt{y}.\\
 		\texttt{Expr taylorSeries(const Expr \& x, const Expr \& a, const int n) const }\\
			\hspace{1cm}\textit{It returns elements, up to }\texttt{n}\textit{-th  
			differentiation, from Taylor series by }\texttt{x}\textit{ in point }\texttt{a}.\\
		\texttt{Expr \&	diff(const Expr \& x)}\\
			\hspace{1cm}\textit{Differentiation with respect to }\texttt{x}.\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1228}%
\begin{figure}\centering
\begin{description}  		
  \item[Auxiliary functions] \hfill \\
		\texttt{Ex * innerCopy()const }\\
		 	\hspace{1cm}\textit{Copying of expressions.}\\
 		\texttt{std::string tree()const }\\
			\hspace{1cm}\textit{Transformation of expressions into std::string, that shows expressions as n-ary trees.}\\
 		\texttt{void sign(const Sign \&)\\
 				Sign sign()const }\\
			\hspace{1cm}\textit{Sign management.}\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1554}%
\begin{figure}\centering
\begin{description}  		
  \item[Comparison] \hfill \\
		\texttt{static bool addLessThan(const~Ex~*~L, const~Ex~*~R, const~bool~compareSignSym~=~true)\\}
	 		\hspace{1cm}\textit{Special comparison for elements of additions.\\}
		\texttt{static bool mulLessThan(const~Ex~*~L, const~Ex~*~R, const~bool~compareSignSym~=~true)\\}
 			\hspace{1cm}\textit{Special comparison for elements of multiplications.\\}
 		\texttt{static bool auxLessThan(const~Ex~*~L, const~Ex~*~R, const~bool~compareSignSym~=~true)}\\
		 	\hspace{1cm}\textit{General comparison.}\\
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4083}%
$ 6x(3-4y) \longrightarrow x(3-4y)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4085}%
$ (x+y^2)^3 \longrightarrow x+y^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4087}%
$ numbers < variables < powers < additions < multiplications < functions$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1585}%
\begin{figure}\centering
\begin{description}  		
  \item[Compatibility] \hfill \\
		\texttt{static compatibility compatibilityForAddition(const~Ex~*~L, const~Ex~*~R)\\}
	 		\hspace{1cm}\textit{Is it possible to simplify the sum of input expressions?\\}
		\texttt{static compatibility compatibilityForMultiplication( const~Ex~*~L, const~Ex~*~ R)\\}
	 		\hspace{1cm}\textit{Is it possible to simplify the multiplication of input expressions?\\}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1606}%
\begin{figure}\centering
\begin{description}  		
  \item[Operators] \hfill \\
		\texttt{Expr operator+(const Expr \&, const Expr \&)\\
				Expr operator-(const Expr \&, const Expr \&)\\
				Expr operator*(const Expr \&, const Expr \&)\\
				Expr operator\^{ }(const Expr \&, const Expr \&)\\
				Expr operator/(const Expr \&, const Expr \&)\\
				Expr Power(const Expr \&, const Expr \&)\\
		}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1616}%
\begin{figure}\centering
\begin{description}  		
  \item[Member functions of Operations] \hfill \\
		\texttt{static Expr operatorAdd(const Expr \&, const Expr \&)\\
				static Expr operatorSub(const Expr \&, const Expr \&)\\
				static Expr operatorMul(const Expr \&, const Expr \&)\\
				static Expr operatorDiv(const Expr \&, const Expr \&)\\
				static Expr operatorPow(const Expr \&, const Expr \&) \\
		}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1627}%
\begin{figure}\centering
\begin{description}  		
  \item[Member functions of Operations] \hfill \\
		\texttt{static Ex * addition(const Ex *, const Ex *)\\
				static Ex * subtraction(const Ex *, const Ex *)\\
				static Ex * multiplication(const Ex *, const Ex *)\\
				static Ex * division(const Ex *, const Ex *)\\
				static Ex * power(const Ex *, const Ex *)\\
		}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1635}%
\begin{figure}\centering
\begin{description}  		
  \item[Member functions of Operations] \hfill \\
		\texttt{static Ex * addition(Ex * \&, Ex * \&, const allocationPolicy)\\
				static Ex * subtraction(Ex * \&, Ex * \&, const allocationPolicy)\\
				static Ex * multiplication(Ex * \&, Ex * \&, const allocationPolicy)\\
				static Ex * division(Ex * \&, Ex * \&, const allocationPolicy)\\
				static Ex * power(Ex * \&, Ex * \&, const allocationPolicy)\\
		}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1646}%
\begin{figure}\centering
\begin{description}  		
  \item[Simplification of powers] \hfill \\
    $\text{Let A,B and C be expressions.}$\\
    \begin{itemize}	
	\item$A^0 \longrightarrow 1 $\\
	\item$A^1 \longrightarrow A $\\
	\item$1^{A} \longrightarrow 1$\\
	\item$0^{A} \longrightarrow 0$\\
	\item$number^{integer} \longrightarrow number$\\
	\item$number^{-integer} \longrightarrow \frac{1}{number}$\\
	\item$(-A)^{B} \longrightarrow (-1)^{B}A^{B}$\\
	\item$(A)^{B^C} \longrightarrow A^{BC}$\\
	\item$(AB)^C \longrightarrow A^CB^C$\\
	\end{itemize}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1681}%
\begin{figure}\centering
\begin{description}  		
  \item[Simplification of addition] \hfill \\
    $\text{Let A,B and C be expressions and x, y, z numbers.}$\\
    \begin{itemize}	
	\item$A+A \longrightarrow 2A $\\
	\item$xA+yA \longrightarrow zA,\ where\ z = x+y$\\
	\item$A+0\ or\ 0+A \longrightarrow A$\\
	\end{itemize}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1691}%
\begin{figure}\centering
\begin{description}  		
  \item[Simplification of multiplication] \hfill \\
    $\text{Let A,B and C be expressions and x,y,z numbers.}$\\
    \begin{itemize}	
	\item$1*A\ or\ A*1 \longrightarrow A $\\
	\item$0*A\ or\ A*0 \longrightarrow 0 $\\
	\item$-1*A\ or\ A*(-1) \longrightarrow -A $\\
	\item$AA \longrightarrow A^2 $\\
	\item$A^BA^C \longrightarrow A^{B+C}$\\
	\end{itemize}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4122}%
$ f(x)^{g(x)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4124}%
$\displaystyle \left(f(x)^{g(x)}\right)' = 
f(x)^{g(x)}\left(g'(x)Ln\left(f(x)\right)+g(x)\frac{f'(x)}{f(x)}\right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4126}%
$\displaystyle \left(f(x)^{g(x)}\right)'=
\left(e^{Ln\left(f(x)^{g(x)}\right)}\right)'=
\left(e^{g(x)Ln\left(f(x)\right)} \right)'.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1891}%
\begin{figure}		\texttt{enum $\lbrace$\  \\
				INCOMPATIBLE,}\textit{ //Relationship is not detected.}\\
		\texttt{NUMBER\_NUMBER,}\textit{ //Both compared expressions are numbers.}\\
		\texttt{PLAIN\_PLAIN,}\textit{ //Expressions are compatible and neither is multiple.}\\
		\texttt{MULTIPLE\_MULTIPLE,}\textit{ //Expressions are multiple.}\\
		\texttt{PLAIN\_MULTIPLE,}\textit{ //The second expression is a multiple of the first.}\\
		\texttt{MULTIPLE\_PLAIN,}\textit{ //The first expression is a multiple of the second.}\\
		\texttt{BASE\_BASE,}\textit{ //Both expressions are powers and their bases are compatible.}\\
		\texttt{BASE\_PLAIN,}\textit{ //The first expression is a power and its base is compatible with the second expression.}\\
		\texttt{PLAIN\_BASE,}\textit{ //The first expression is compatible with the base of the second expression that is a power.}\\
		\texttt{$\rbrace$\  compatibility;}\\
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1917}%
\begin{figure}		\texttt{enum $\lbrace$\  \\
				EX,}\textit{ //general expressions -- class Ex}\\
		\texttt{NUM,}\textit{ //numbers -- class Number}\\
		\texttt{SYM,}\textit{ //variables -- class Sym}\\
		\texttt{POW,}\textit{ //powers -- class Pow}\\
		\texttt{ADD,}\textit{ //addition -- class Add}\\
		\texttt{MUL,}\textit{ //multiplications -- class Mul}\\
		\texttt{FX,}\textit{ //functions -- class Fx}\\
		\texttt{$\rbrace$\  type\_info;}\\
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1955}%
\begin{figure}		\begin{verbatim}

		namespace sympycpp {	
		    void containerSort(std::list<Ex *> & l,
                       bool (* lessThan)(const Ex *, const Ex *)) {
		       l.sort(lessThan);
		    }
		    void containerSort(std::vector<Ex *> & v, 
                       bool (* lessThan)(const Ex *, const Ex *)) {
		       sort(v.begin(), v.end(), lessThan);
		    }
		}\end{verbatim}

	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4149}%
$ <0,2\pi)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4152}%
$ \pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1986}%
\begin{figure}\centering
\begin{description}  		
  \item[Length of reports] \hfill \\
   \begin{description}
		\item [short report] \hfill \\
		The report consists of the number of the~test and 
		the number of the line in a file where the~test is located.
		\item [long report] \hfill \\
		An~actual textual form of the tested expression and 
		a~required textual form of this expression is added to the short report.
  \end{description}
  \item[Levels of reports] \hfill \\
  \begin{description}
		\item [level 0] \hfill \\
		Correct expressions do not produce any message and 
		incorrect expressions produce the~long report.
		\item [level 1] \hfill \\
		Both cases  produce the short reports.
		\item [level 2] \hfill \\
		Correct expressions produce the short form, 
		incorrect expressions produce the long form of the report.
		\item [level 3] \hfill \\
		Both cases  produce the long reports.
  \end{description}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1997}%
\begin{figure}
% latex2html id marker 1997
\centering
\begin{description}  		
  \item[Abilities of TestX] \hfill \\
  \begin{enumerate}
  \renewedcommand{labelenumi}{(\alph{enumi})}
		\item\texttt{TestX(const int voice = 3, const bool tree = false)}\\
		 	\hspace{1cm}\textit{Constructor that enables the setup a level of 
		 	reports (voice) and a possibility of the preview of the tree representation.}\\
 		\item\texttt{void setTree(const bool)\\
 					 bool setVoice(const int)}\\
			\hspace{1cm}\textit{Setup of the preview of the tree representation and levels of reports.}\\
 		\item\texttt{void test(const Expr \& e, const std::string eStr, const int line = -1, const int nT = 0)}\\
			\hspace{1cm}\textit{Test function.}\\
	\end{enumerate}
\end{description}
	\vspace{-0.5cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlfigureA{figure2151}%
\begin{figure}\begin{description}  		
  \item[Bug in Wolfram Mathematica 7] \hfill \\
		\begin{footnotesize}\texttt{In[5]:=}~\end{footnotesize}\textbf{Solve[((x - 1)*(x\^{ }2 - 3*x + 2))/(x - 1) == 0, x]}\\
		\begin{footnotesize}\texttt{Out[5]=}\end{footnotesize} \{\{x -$>$\  1\}, \{x -$>$\  2\}\}
\end{description}  
	\vspace{-5mm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4183}%
$ 2xyzw\ldots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4185}%
$ 0*anything = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4198}%
$ (a + b + c)^{100}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4200}%
$ (a + b + c)^{278}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4202}%
$ (a + b + c)^{477}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4204}%
$ (a + a(b-c) + c)^{73}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4206}%
$ (a + a(b-c)a(b+c) + c)^{83}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4208}%
$ (a + ab-ac + c)^{77}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4210}%
$ (a + a^2b^2 - 2a^2bc + a^2c^2 + c)^{37}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4212}%
$ (a + b + c + d + e + f + g )^{15}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4309}%
$ sin(a)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4312}%
$ a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4316}%
$ b-2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4325}%
$ \frac{a^x}{cos(a)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4327}%
$ 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4331}%
$ sin(cos(a^3))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\appendix
\stepcounter{chapter}
\stepcounter{chapter}


\newtheorem{bin}[section]{Theorem}%

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4390}%
$ k\in \mathbb{N}, \  a, b \in \mathbb{R}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4392}%
$ (a+b)^k = \sum_{i=0}^{k}\binom{k}{i}a^ib^{k-i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4394}%
$ \binom{k}{i} = \frac{k!}{(k-i)!i!}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}



\newtheorem{mult}[section]{Theorem}%

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4398}%
$ n \geq 2, \  k\in \mathbb{N}, \  a_1,a_2,\ldots,a_n \in \mathbb{R}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4400}%
$ (a_1+a_2+\ldots+a_n)^k = $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4402}%
$ = \sum_{\forall k_1, \ldots, k_n : k_1+\ldots+k_n = k}\binom{k}{k_1, 
\ldots, k_n}{a_1}^{k_1}\ldots{a_n}^{k_n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4404}%
$ \binom{k}{k_1, \ldots, k_n} = 
\frac{k!}{k_1!\ldots k_n!}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}



\newtheorem{taylor}[section]{Definition}%

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4410}%
$ \sum_{k=0}^\infty\frac{f^{(k)}(a)}{k!}(x-a)^k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
